What is the derivative of f(x)=(x^3-1x^2+2)/(x^2) ?

The derivative of f(x)=(x^3-1x^2+2)/(x^2) is (x^3-4)/(x^3)

What is the first derivative of f(x)=(x^3-1x^2+2)/(x^2) ?

The first derivative of f(x)=(x^3-1x^2+2)/(x^2) is (x^3-4)/(x^3)

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derivative of

f (x) = \frac{x ^{3} - 1 x ^{2} + 2}{x ^{2}}

\frac{x ^{3} - 4}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} - 1 \cdot x ^{2} + 2}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{3} - 1 \cdot x ^{2} + 2 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{3} - 1 \cdot x ^{2} + 2 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{3} - 1 \cdot x^{2} + 2) = 3 x^{2} - 2 x

\frac{d}{d x} (x^{2}) = 2 x

= \frac{( 3 x ^{2} - 2 x ) x ^{2} - 2 x ( x ^{3} - 1 \cdot x ^{2} + 2 )}{( x ^{2} ) ^{2}}

Simplify

\frac{( 3 x ^{2} - 2 x ) x ^{2} - 2 x ( x ^{3} - 1 \cdot x ^{2} + 2 )}{( x ^{2} ) ^{2}} : \frac{x ^{3} - 4}{x ^{3}}

= \frac{x ^{3} - 4}{x ^{3}}

\int (x x + 3) d x

\frac{\partial}{\partial x} (x^{4} + y^{4} + 3 x^{2} y^{3})

13 + 2 x - x^{2}, 3 x + 1

f (x) = (x + 1)^{2 x}

\frac{x}{a}

What is the derivative of f(x)=(x^3-1x^2+2)/(x^2) ?
The derivative of f(x)=(x^3-1x^2+2)/(x^2) is (x^3-4)/(x^3)
What is the first derivative of f(x)=(x^3-1x^2+2)/(x^2) ?
The first derivative of f(x)=(x^3-1x^2+2)/(x^2) is (x^3-4)/(x^3)